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Model for Covid-19 in the US

official statement Using some assumptions driven from recent data and current response rate, I have built a fairly simple model to predict the number of COVID-19 cases that will be seen in the U.S.

dose of chloroquine tablet The model starts with Seattle which reported its first case around Jan 21st.  It didn’t go into an emergency state till the end of February.

The model assumes an average rate of infection after the average incubation period.  It also assumes a ratio of local infection and infections that travel to other areas. This leads to the model’s idea of clusters.  When an infection travels to another area, it creates a cluster.  In a cluster, once a certain number of cases are detected, the area typically goes into a state of lockdown and emergency.   The result of this should be a quickly declining spread and stopping of creating of additional clusters. The model assumes a more and more aggressive reaction response, based on recent data where some places when into emergency or lockdown mode after just 4 reported cases.

The further modeling of areas that are in actual or virtual lockdown is the difficult part as there is no clear data on how quickly the spread will stop. 

The model shows that currently there are close to 19,000 people in the US that are already infected.  Most of them were infected in the 1st week of March and thus are starting to show symptoms now. Thus over the next week or so, the number or confirmed cases will rise dramatically from the last reported 2500 or so.

The model estimates that the total number of infected cases will rise to somewhere between 22,000-25,000 after which the transmission will slow down significantly and essentially be contained. It is estimated that this will happen around the second week of April.

Below is a graph of the estimate from the model.

Of course, no one knows exactly what will happen. The model was built was a rather simple, but logical, set of assumptions and was driven by observed data so far in the US and other countries, but this data is what I found on the internet, which in itself is a bit flawed.

Nature

I was in Kentucky visiting friends who took me on a short hike on Berea forest trails. These friends are “bird” people – bird watchers and photographers.  So, on the hike, we would stop often when they heard some bird and they would look up to try and capture a photograph – which I also got into and starting pointing out birds in the canopy of the trees. When I saw them my description limited to “…a small black one there..” or “…a large black one over here…”.  They would look at it and say something like, “…that’s a yellow rumped warbler…” and then my friend would take some pictures with the huge lens attached to his camera.

These are what my “little black birds” really looked like!

They live on a 13 acre farm in rural Kentucky, with a view of a pond and lots of trees and vegetation. When I walked down their stairs to their living room I see five cats looking up at me (they are also “cat” people); in the morning the back yard is full of birds looking for food; in the evening the raccoons come around to their porch and eat all the cat food.

My friend, a close buddy from college, got his first SLR a few years ago and now has become a really good bird photographer.  Just around where he lives, and mostly from his porch itself, he has photographed and identified over 130 different bird species.  Some of these are just magnificent, a few pictures below.

The fact that over 130 species in that area of KY alone was mind boggling – well it turns out there are over 10,000 bird species in the world. Add to that all the different mammals, sea creatures, reptiles and the 10 quintillion insects – and we are reminded how vast the living world of nature is.  Human beings share this earth with all these living creatures and only represent one species out of tens of millions.  While it is no doubt that we are the dominant species in modifying, building creating and overcoming our environment to make it easier for us to live, we still only represent a small fraction of all the co-inhabitants of this earth both in numbers and even in actual mass. 

All this is a constant reminder that humans, representing such a small portion of all living beings, have http://turnyourdayaround.com/accuneb no right to destroy the environment, the nature of this world, due to their activities. As Spinoza says, God is Nature and Nature is God. So, let us never forget the environment and our duty to protect it

Action and dharma

Our actions are what define us.  Just thoughts, however good they may be, unless proceeded by action, remain just theoretical.

The philosophical study of action and its motives dates back to Ancient Greece and India.  To be clear, my reference to “action” is intentional action or things that people genuinely do.  

As Aristotle said, in order for a man to perfect his humanity, he must be the best man he can be. To be his manly best, a man not only needed to cultivate proper intentions and an appropriate disposition, but put those intentions into real virtuous action.

In ancient Indian philosophy, the goal of the early portion of the Vedas is action, in particular moral or dharmic.  A human being is defined by his or her actions and the actions are what defines the persons’ dharma.

Even if we aim for virtuous actions, the world has become so complicated that it is hard to know if the action is truly virtuous.  The degrees of freedom between an action and it’s consequence or consequences can be so numerous that it is impossible to know if the action was good. This problem of unintended consequences could have the effect of making almost all actions non-virtuous. So, what is one to do? The only real practical answer is to still act in good faith within one’s cognitive visibility or horizon. Otherwise if we try and analyze too many possibilities it could result in paralysis by analysis.

I personally have always tried to act in a way that is purposeful.  My actions are usually preceded by rational thought and logic, which is somewhat consequential or utilitarian in that I would try and evaluate the course of action by what it can achieve vis a vis other choices.  This has largely been my principle, my dharma and has mostly served me well and it suited my predominantly analytical mindset.

But not too long ago there has been somewhat of a change.  Recently an old colleague asked our college class group for money to help his son’s education, having fallen in difficult times in his career. This was not the first time he had asked, and we all came to know that he has asked other family and friends for money in the past. I thought about this – rationally and logically – and argued against contributing, citing that this has become a ritual and habit of his, that there are better places to put my money, why can’t he send his son to a college within their means and so on and so forth. It all made sense based on the principles that have normally governed my actions.  Then suddenly I contributed. Not out of guilt or coercion, rather it dawned on me that all my analysis was really to serve myself – the only thing that mattered at that time was there was a friend in need and that I could take a small action to help. Period,

Soon after that another incident happened in which an aging family member was raising a fund to support their special needs son so he can live in an appropriate institution.  The immediate analytic assessment was why have they not been planning for this for the last fifty years and so on.  But I stopped short in my tracks and chided myself –  who was I to question their life and their lack of setting enough aside for their son, neither do I know the complete picture and neither am I qualified to judge them.  They have a need and I can help, so I should act, and I did.

The analysis, the justification, the rationalization is sometimes how we attach ourselves to the results or fruits of the action – it seems like we do that more for ourselves, thus in a way it is for selfish means.  While action based on the analysis of the results is clearly still needed in order to achieve certain goals, needs and comforts in life, it was truly liberating to simply act without any analysis, purely on the basis of the need to act, completely without attachment.  I am sure in life there is a balance of the two, which I am yet to figure out. I am not planning on abandoning the dharma that has served me, but the new dharma, if I may call it that, has been satisfying.

Dharma truly is subtle.

Skew Vega

Skew Vega is the exposure of an options portfolio to a change in the implied vol skew, e.g. change in the risk reversal level. While teaching my daughter trigonometry, I realized that using some basic trigonometry, I could easily calculate the Skew vega in the case where there is no functional form (parameterized) volatility surface. Here is a simple and elegant model to calculate the skew vega

Calculating Skew Vega model